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“Magnets that accelerate particles”… the only particles that a magnetic field can accelerate are magnetic monopoles, and they are yet to be discovered.

The lhc, as well as all accelerators, use electric field to accelerate particles. Supraconcting RF cavities.

Since it’s not very practical to work with 7000 billion volts, physicists use magnets to bend particles paths so they pass several several times through the rf cavities.

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Unless all charge is stationary, you'll have both electric and magnetic fields.

Moving charge generates a magnetic field, and interacts with external magnetic fields. Charged particles will accelerate while spiralling around magnetic field lines. The aurora is caused by charged particles bouncing back and forth along magnetic field lines between the pinch points at the poles.